City had been anaemic, their creative forces anonymous, when FC Copenhagen goalkeeper Jesper Christiansen allowed Nedum Onuoha's shot to squirm under his body and roll over the line to give Hughes's side the lead.
Nothing is simple for the blue half of Manchester, though, and that set the tone for the game. Ailton equalised with a soft header, before Ulrik Laursen misjudged Shaun Wright-Phillips' hopeful cross, allowing Stephen Ireland to slot home.
That should still be enough to see City through, despite Martin Vingaard heading home unmarked in injury time to take the gloss off an away game Hughes's side, vastly improved on their domestic away form, should have won.
Hughes said: 'We would have been happy before the game two goals away from home and a decent performance but to let them back into it at the death is disappointing.
'We had plenty of chances to put the game beyond them but we're still in a good position to finish the job next week. We had much more resolve than in recent weeks and hopefully that will give us something to take to Anfield on Sunday.
'We showed if teams give us the space we can exploit it. I was really pleased with our attitude and our speed on the break. When we play like that we can worry anyone.'
Prior to Christiansen's moment of horror, the game had been to a lively contest what the giant mural covering one end of the Parken Stadion was to an actual crowd.
Given the conditions, it was little surprise the opening goal of a limp game on a newly-laid pitch not dissimilar to an ice rink in Copenhagen's sub-zero winter, came as a result of a moment Christiansen will be desperate to forget. Ireland slipped Onuoha through and his tame shot somehow crept under the distraught Christiansen and across the line, barely rippling the net.
'Nedum insists he gave the goalkeeper the eyes and that's why he scored,' said Hughes. 'We'll have to take his word on that one.'
It was not until after half time that Copenhagen rallied. Atiba Hutchinson and Zdenek Pospech both threatened before City's set-piece curse returned, Ailton all alone in the six-yard box to nod home Thomas Kristensen's corner.
It did not take long for City to regain their lead, Ireland, the man Copenhagen boss Stale Solbakken identified as more of a threat than Robinho before the game, sweetly firing the ball home after Ulrik Laursen misjudged the bounce of Shaun Wright-Phillips' hopeful cross.
That should have been City's cue to put the game and the tie beyond doubt, but Wright-Phillips and, more culpably, Robinho wasted gilt-edged chances to kill the game off before debutant Vingaard rose unmarked at the far post to meet Dame N'Doye's cross and give the Danish side a glimmer of hope in the return.